The power of four tests of autocorrelation in the linear regression model

The power of each of four tests of first-order autocorrelation in the linear regression model is determined for a simple and multiple regression model whose parameters are presumed to be known. The tests are: Durbin-Watson bounds test, a test based on Theil's best linear unbiased scalar estimator, a test devised by Abrahamse, Koerts and Louter, and an exact test devised by Durbin.For positive values of the coefficient of autocorrelation the Durbin-Watson bounds test is generally better than the tests based on the estimator proposed by Abrahamse, Koerts and Louter, the best linear unbiased scalar estimator, and the Durbin exact test. For negative values of the coefficient of autocorrelation, the pattern of results is mixed for all four test procedures. A byproduct of these experiments is the demonstrated feasibility of enumerating the distribution of the Durbin-Watson test statistic for any regression matrix and thus eliminating the region of indeterminacy from the Durbin-Watson test procedure.     

Testing for autoregressive against moving average errors in the linear regression model

This paper presents a new approach to hypotheses testing problems which are non-nested in the classical sense and which concern the covariance matrix of the disturbance vector of the linear regression model. In particular, the application of the approach to testing for AR(1) disturbances against MA(1) disturbances is explored in some detail. Practical difficulties are discussed and selected upper bounds for the test's five percent significance points are tabulated. The small sample power of four versions of the new test are compared empirically and a clear conclusion is made in regard to the best overall test.     

Sparse linear models and l1-regularized 2SLS with high-dimensional endogenous regressors and instruments

We explore the validity of the 2-stage least squares estimator with $l_1$-regularization in both stages, for linear triangular models where the numbers of endogenous regressors in the main equation and instruments in the first-stage equations can exceed the sample size, and the regression coefficients are sufficiently sparse. For this $l_1$-regularized 2-stage least squares estimator, we first establish finite-sample performance bounds and then provide a simple practical method (with asymptotic guarantees) for choosing the regularization parameter. We also sketch an inference strategy built upon this practical method.     

The alternative Durbin-Watson test: An assessment of Durbin and Watson's choice of test statistic

This paper examines Durbin and Watson's (1950) choice of test statistic for their test of first- 0order autoregressive regression disturbances. Attention is focused on an alternative statistic, d'. Theoretical and empirical power properties of the d' test are compared with those of the Durbin-Watson test. The former is found to be locally best invariant while the latter is approximately locally best invariant. The d' test is also found to be more powerful than its counterpart against negative autocorrelation and for small values of the autocorrelation coefficient against positive autocorrelation. Selected bounds for significance points of d' are tabulated.     

On efficient estimation of the ordered response model

In this paper, we derive efficiency bounds for the ordered response model when the distribution of the errors is unknown. Furthermore, we develop an estimator that is efficient under suitable conditions. Interestingly, neither the bounds nor the estimator are trivial extensions of what has been proposed in the literature for the binary response model. The estimator is composed of quadratic B-splines, and estimation is performed by the method of sieves. In addition, the estimator of the distribution function is restricted to be a proper distribution function. An empirical example on the effect of fees on attendance rates at universities and community colleges is also included; we get substantively different results by relaxing the assumption that the distribution of the errors is normal.     

Set identification via quantile restrictions in short panels

This paper studies the identifying power of conditional quantile restrictions in short panels with fixed effects. In contrast to classical fixed effects models with conditional mean restrictions, conditional quantile restrictions are not preserved by taking differences in the regression equation over time. This paper shows however that a conditional quantile restriction, in conjunction with a weak conditional independence restriction, provides bounds on quantiles of differences in time-varying unobservables across periods. These bounds carry observable implications for model parameters which generally result in set identification. The analysis of these bounds includes conditions for point identification of the parameter vector, as well as weaker conditions that result in point identification of individual parameter components.     

Concept‐Based Bayesian Model Averaging and Growth Empirics

In specifying a regression equation, we need to specify which regressors to include, but also how these regressors are measured. This gives rise to two levels of uncertainty: concepts (level 1) and measurements within each concept (level 2). In this paper we propose a hierarchical weighted least squares (HWALS) method to address these uncertainties. We examine the effects of different growth determinants taking explicit account of the measurement problem in the growth regressions. We find that estimates produced by HWALS provide intuitive and robust explanations. We also consider approximation techniques which are useful when the number of variables is large or when computing time is limited.     

Efficiencies of Rounded Optimal Approximate Designs for Small Samples

Optimal exact designs are notoriously hard to study and only a few of them are known for polynomial models. Using recently obtained optimal exact designs (I mhof , 1997), we show that the efficiency of the frequently used rounded optimal approximate designs can be sensitive if the sample size is small. For some criteria, the efficiency of the rounded optimal approximate design can vary by as much as 25% when the sample size is changed by one unit. The paper also discusses lower efficiency bounds and shows that they are sometimes the best possible bounds for the rounded optimal approximate designs.     

Analyzing an extension of the isotonic regression problem

In this paper an extension of the classical problem of isotonic regression is first considered. This problem extends the criterion of minimizing convex functions by considering a more general situation. To solve this problem, the max–min formulae are extended by means of the concept of change-level vector, leading to new formulae and algorithms. Moreover, we will find explicit expressions for every isotonic regression when the solution is not unique by considering both max–min and change-level formulae. An immediate implication from the considered extension is that bounds for isotonic regressions can be stated. Furthermore, the problem of finding solutions within a horizontal band in the plane can now be solved. Finally, some practical applications are discussed.     

A Simple Test for Convergence of Metropolitan Income in the United States

The prevalent test for income convergence used in many recent studies of convergence across spatial economic units in the United States is to use a regression equation in which income growth is regressed against the initial level of income (this is known as β convergence). That method, however, has been crtiticized as an instance of Galton's fallacy of regression. We devise a simple test for the income β-convergence hypothesis which does not suffer from “Galton's fallacy” and apply it to all of the metropolitan areas of the United States for the period 1969–1995. For the test we use two income measures: per capita personal income and average wages. Our results conclusively support convergence of per capita personal income and of wage per worker for metropolitan areas in the United States. We also test for σ convergence, the hypothesis of diminishing dispersion in income among places over time, and find no support for the hypothesis.     

Competitive On-line Statistics

A radically new approach to statistical modelling, which combines mathematical techniques of Bayesian statistics with the philosophy of the theory of competitive on-line algorithms, has arisen over the last decade in computer science (to a large degree, under the influence of Dawid's prequential statistics). In this approach, which we call "competitive on-line statistics", it is not assumed that data are generated by some stochastic mechanism; the bounds derived for the performance of competitive on-line statistical procedures are guaranteed to hold (and not just hold with high probability or on the average). This paper reviews some results in this area; the new material in it includes the proofs for the performance of the Aggregating Algorithm in the problem of linear regression with square loss.     

一元线性回归方程有关检验问题的研究

文章从数学角度给出T检验、F检验、相关系数的显著性检验三者一致性证明;明确了决定系数和残差分析在诊断回归效果中的作用。利用三spss软件实例分析,使得一元线性回归问题中的几种检验间的关系及作用进一步明确。     

直接甲醇提取高效液相色谱法测定BHA、BHT

目的:建立一种油脂和食品中用甲醇将BHA、BHT溶解出来,在拟定的测定参数下,直接进样分离,检测的方法。方法:采用C18(250×4.60mm)色谱柱,流动相为0.02mol/L乙酸铵-甲醇(95:5体积比),流速:1ml/min,紫外检测波长280nm;进样量20μl;外标法定量。结果:方法标准曲线线性良好,BHA回归方程为:Y=2.127X-3.24,回归系数r=0.9997;BHT回归方程为:Y=60.32X+0.70,回归系数r=0.9998。添加质量浓度为0.01%～1.0%时BHA的回收率为93.6%～103.9%,BHT的回收率为97.5%～108.5%。结论:该方法操作简单、准确、回收率高,精密度良好,重现性好,可用于食用油、饼干等食品中BHA、BHT的测定。     

Effective sub-simulation-free upper bounds for the Monte Carlo pricing of callable derivatives and various improvements to existing methodologies

We present a new non-nested approach for computing additive upper bounds for callable derivatives using Monte Carlo simulation. It relies on the regression of Greeks computed using adjoint methods. We also show that it is possible to early terminate paths once points of optimal exercise have been reached. A natural control variate for the multiplicative upper bound is introduced which renders it competitive to the additive one. In addition, a new bi-iterative family of upper bounds is introduced which takes a stopping time, an upper bound, and a martingale as inputs.     

A new bounded log-linear regression model

In this paper we introduce a new regression model in which the response variable is bounded by two unknown parameters. A special case is a bounded alternative to the four parameter logistic model. The four parameter model which has unbounded responses is widely used, for instance, in bioassays, nutrition, genetics, calibration and agriculture. In reality, the responses are often bounded although the bounds may be unknown, and in that situation, our model reflects the data-generating mechanism better. Complications arise for the new model, however, because the likelihood function is unbounded, and the global maximizers are not consistent estimators of unknown parameters. Although the two sample extremes, the smallest and the largest observations, are consistent estimators for the two unknown boundaries, they have a slow convergence rate and are asymptotically biased. Improved estimators are developed by correcting for the asymptotic biases of the two sample extremes in the one sample case; but even these consistent estimators do not obtain the optimal convergence rate. To obtain efficient estimation, we suggest using the local maximizers of the likelihood function, i.e., the solution to the likelihood equations. We prove that, with probability approaching one as the sample size goes to infinity, there exists a solution to the likelihood equation that is consistent at the rate of the square root of the sample size and it is asymptotically normally distributed.     

Treatment effect bounds: An application to Swan–Ganz catheterization

We reanalyze data from the observational study by Connors et al. (1996) on the impact of Swan–Ganz catheterization on mortality outcomes. The study by Connors et al. (1996) assumes that there are no unobserved differences between patients who are catheterized and patients who are not catheterized and finds that catheterization increases patient mortality. We instead allow for such differences between patients by implementing both the instrumental variable bounds of Manski (1990), which only exploits an instrumental variable, and the bounds of Shaikh and Vytlacil (2011), which exploit mild nonparametric, structural assumptions in addition to an instrumental variable. We propose and justify the use of indicators of weekday admission as an instrument for catheterization in this context. We find that in our application, the Manski (1990) bounds do not indicate whether catheterization increases or decreases mortality, where as the Shaikh and Vytlacil (2011) bounds reveal that at least for some diagnoses, Swan–Ganz catheterization reduces mortality at 7 days after catheterization. We show that the bounds of Shaikh and Vytlacil (2011) remain valid under even weaker assumptions than those described in Shaikh and Vytlacil (2011). We also extend the analysis to exploit a further nonparametric, structural assumption–that doctors catheterize individuals with systematically worse latent health–and find that this assumption further narrows these bounds and strengthens our conclusions. In our analysis, we construct confidence regions using the methodology developed in Romano and Shaikh (2008). We show in particular that the confidence regions are uniformly consistent in level over a large class of possible distributions for the observed data that include distributions where the instrument is arbitrarily “weak”.     

A Lower Bound for the Centered <Emphasis Type="Italic">L</Emphasis><Subscript>2</Subscript>-Discrepancy on Asymmetric Factorials and its Application

The role of uniformity measured by the centered L ₂-discrepancy (Hickernell 1998a) has been studied in fractional factorial designs. The issue of a lower bound for the centered L ₂-discrepancy is crucial in the construction of uniform designs. Fang and Mukerjee (2000) and Fang et al. (2002, 2003b) derived lower bounds for fractions of two- and three-level factorials. In this paper we report some new lower bounds for the centered L ₂-discrepancy for a set of asymmetric fraction factorials. Using these lower bounds helps to measure uniformity of a given design. In addition, as an application of these lower bounds, we propose a method to construct uniform designs or nearly uniform designs with asymmetric factorials.     

Confidence bounds for the mean in nonparametric multisample problems

In auditing practice it often occurs that a statement regarding the accounting error in a population consisting of several subpopulations has to be made. As the relative proportion of errors can differ dramatically across these subpopulations, it is desirable to take independent fixed-size dollar-unit samples from each of them, as this often leads to lower variability compared with dollar-unit sampling from the whole population. It also occurs that the results of the separate investigations of, e.g. different branches of one company need to be combined to make a statement on the bookkeeping quality in general.
The problem of estimating the total accounting error is thus related to the problem of estimating linear combinations of the mean values corresponding to several families of identically distributed independent random variables.
In this article, we propose several confidence upper bounds for such linear combinations based on Hoeffding-type inequalities and show how they can be applied to the actual auditing problems. Simulation results comparing these modifications to the Hoeffding-based bounds for the one-sample case are also provided. It must be emphasized that the technique that we propose in this paper is fully justified from a mathematical point of view.
Although the simulations show the proposed bounds to be highly conservative, they still present great interest, since we are not aware of any other method for estimation of the total accounting error in the multisample setting. Moreover, it is shown that significant improvements are hardly possible given the present conditions.     

Inference on an extended Roy model,with an application to schooling decisions in France

This paper considers the identification and estimation of an extension of Roy’s model (1951) of sectoral choice, which includes a non-pecuniary component in the selection equation and allows for uncertainty on potential earnings. We focus on the identification of the non-pecuniary component, which is key to disentangling the relative importance of monetary incentives versus preferences in the context of sorting across sectors. By making the most of the structure of the selection equation, we show that this component is point identified from the knowledge of the covariate effects on earnings, as soon as one covariate is continuous. Notably, and in contrast to most results on the identification of Roy models, this implies that identification can be achieved without any exclusion restriction nor large support condition on the covariates. As a by-product, bounds are obtained on the distribution of the ex ante   monetary returns. We propose a three-stage semiparametric estimation procedure for this model, which yields root-n$n$ consistent and asymptotically normal estimators. Finally, we apply our results to the educational context, by providing new evidence from French data that non-pecuniary factors are a key determinant of higher education attendance decisions.     

Identification issues in the public/private wage gap,with an application to Italy

This paper reviews some of the standard assumptions that are imposed in order to estimate the average public/private wage gap and that are mainly related to the possible selection of the sector. There are two contributions to the existing public/private wage gap literature. One is a better understanding of the identified parameters: standard estimators identify a local effect (LATE), which in general cannot be generalized to the entire population, as instead is almost always done. The other is the partial identification of the population average treatment effect, with an instrumental variable. To the best of my knowledge, this is the first paper in this literature that employs bounds. The technique is applied to male workers in Italy. For compliers, LATE estimates a wage advantage from working in the public sector greater than 30%. This return is within the narrowest bounds on the population average treatment effect that are consistent even with a much smaller gap (about 15% or more).